Research map / Optimization / Nonconvex and smooth optimization
Two-Scale Gradient Descent Ascent Dynamics Finds Mixed Nash Equilibria of Continuous Games: A Mean-Field Perspective
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| two-scale (finite scale ratio eta) Mean-Field GDA in fast ascent regime with eta set to 2*lambda_LS*kappa^2*Diam(Y)^2/gamma | Mean-Field GDA for entropy-regularized two-player zero-sum game · entropy-regularized objective E_tau (fixed temperature) | exponential convergence rate of Lyapunov function L | Helped |
| two-scale Mean-Field GDA in fast descent regime (finite small eta) versus quasi-static eta=0 or infinity limits | Mean-Field GDA · entropy-regularized objective E_tau (fixed temperature) | convergence guarantee | Helped |
| annealing temperature tau_t = xi/log t with eta_t scaled as M t^{xi*/xi}/(log t)^2 (fast ascent) | annealed Mean-Field GDA · unregularized objective E_0, Nikaido-Isoda error | NI(mu_t, nu_t) upper bound | Helped |
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